A single tap can fill a tank in 6 hours. After the tank is half full, three additional identical taps are opened. How long will it take to fill the tank completely?

Explanation

One tap fills the entire tank in 6 hours, so it fills half the tank in 3 hours. When the tank is half full, three more taps identical to the first are opened, making a total of 4 taps. The combined filling rate of 4 taps is 4 × (1/6) = 2/3 of the tank per hour. The remaining half of the tank needs to be filled at this rate, so time required is (1/2) ÷ (2/3) = 3/4 hours, or 45 minutes. Therefore, total time to fill the tank is 3 hours + 45 minutes = 3 hours 45 minutes.